{
  "id": "2412.04953",
  "version": "v1",
  "published": "2024-12-06T11:11:33.000Z",
  "updated": "2024-12-06T11:11:33.000Z",
  "title": "Upper semi-continuity of metric entropy for diffeomorphisms with dominated splitting",
  "authors": [
    "Chiyi Luo",
    "Wenhui Ma",
    "Yun Zhao"
  ],
  "comment": "19pages, all suggestions and comments are welcome",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a $C^{r}$ $(r>1)$ diffeomorphism on a compact manifold that admits a dominated splitting, this paper establishes the upper semi-continuity of the entropy map. More precisely, given a sequence of invariant measures with only positive Lyapunov exponents along a sub-bundle and non-positive Lyapunov exponents along another sub-bundle, the upper limit of their metric entropies is less than or equal to the entropy of the limiting measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-06T11:11:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric entropy",
      "upper semi-continuity",
      "dominated splitting",
      "diffeomorphism",
      "compact manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}